Regular dusting with the brush attachment on a vacuum cleaner should be enough to keep your silk lampshades looking their best. If age or staining cause the shade to require a deeper cleaning, spot treatments followed by a dunk in the bathtub can make your shades look fresh again.
Vacuum the shade.
Remove dust from the shade by vacuuming it off with your vacuum cleaner's brush attachment. Be sure to pull the dust out of all of the pleats and crevices on the shade.
Prepare a bath.
Fill your bathtub or a large clean container with enough warm water to completely cover the shade. Add a scoop of mild laundry detergent designed for babies, or one designed for hand-washing silks and other delicate fabrics. Mix to create sudsy water.
Collect some soapsuds on a soft brush or clean cloth. Use them to gently scrub away any stains or dark spots on the lampshade. Move the brush or cloth in a circular motion.
After spot treating, immerse the entire lampshade in the water, and then swish it up and down. Drain the tub, and then refill it with soapy water again, repeating the process until the lampshade no longer makes the water dirty.
When you're done cleaning, empty the tub or basin and refill it with plain warm water. Dip the lampshade in, pulling it up and down, until soapsuds stop coming out of the shade. You may need to drain and refill the tub several times to get all of the soap out of the shade.
Place the lampshade on a clean towel to dry, or on top of a clothes drying rack.